What is cos A? 15
С
36
B
Enter your answer as a simplified fraction, in
the box
COS A

Step-by-step explanation:

The given triangle, ∆ABC is a right triangle.

To find cos A, we'd need to apply the trigonometric ratio formula, which is cos A = adjacent length/hypotenuse length

From the ∆ given,

AC = adjacent = 15,

BC = opposite = 36

We are not given the hypotenuse length AB.

==>Find the hypotenuse length AB, using the Pythagorean theorem formula:

c² = a² + b²

AB² = 15² + 36² = 225 + 1296 = 1521

AB = √1521

AB = 39

==>Find cos A:

cos A = adjacent/hypotenuse

Adjacent = AC = 15

Hypotenuse = AB = 39

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

answer: i'm not going to give you the answer, but some hints to work it out.

step-by-step explanation: so, if there is a straight line that means that the line angle is 180°. so we subtract the 2 angle measures provided, (15 and 38) from 180. so the answer is 180 - (38 + 15). (you have to solve the equation)